Primer walking is a very common and effective sequencing strategy. In this procedure a primer designed from a known sequence is used to extend sequence information into a previously unknown region. The new sequence information is used to design the next primer and continue the process until the entire sequence of the region of interest is determined. Primer walking has advantages over other sequencing strategies because it does not require multiple cloning steps nor subsequent template preparations, and it is a directed and methodical approach. The primary disadvantages of primer walking include the cost of synthesizing gene specific primers to extend the sequence (mainly because synthesis of each oligonucleotide produces approximately a 1000 fold excess of primer) and the time involved in designing and synthesizing these new primers. These disadvantages could be eliminated if a comprehensive library of pre-existing primers were available. A strategy for high-volume sequencing of cosmid DNAs using a primer library composed of 8-, 9-, or 10-mers was proposed (Studier, F. W. 1989. Proc. Natl. Acad. Sci. USA 86, 6917-6921), while others have proposed synthesizing a library containing a subset of useful octamers or nonamers (Burbelo, P. D. and M. J. Iadarola. 1994. BioTechniques 16, 645-650; Siemieniak, D. R. and J. L. Slightom. 1990. Gene 96, 121-124). The present invention provides the first useful method of developing a library of octamers for primer walking, the first useful octamer library and the first useful employment of the octamer library.